Frequencies, Means, and Crosstabs
Once descriptive statistics are understood, the next step is to explore how values are distributed and how different variables relate to each other.
SPSS provides three powerful tools for this purpose: Frequencies, Means, and Crosstabs. These tools are especially useful when working with categorical and grouped data.
Understanding Frequencies
Frequencies show how often each value or category appears in a dataset. They are most useful for categorical variables, such as gender, department, or response options.
Frequencies help you:
- Understand data distribution
- Identify dominant categories
- Detect unusual or rare values
They also provide percentages, which are easier to interpret than raw counts.
Example: Frequency Distribution
Consider the following dataset of employee departments:
| Employee_ID | Department |
|---|---|
| 801 | IT |
| 802 | HR |
| 803 | IT |
| 804 | Sales |
| 805 | IT |
A frequency table clearly shows how many employees belong to each department.
Using Frequencies in SPSS
To generate frequencies using the menu:
- Go to Analyze → Descriptive Statistics → Frequencies
- Select the categorical variable
- Click OK
SPSS produces counts, percentages, and optional charts.
FREQUENCIES VARIABLES=Department.
Understanding Means
Means summarize numeric data by calculating the average value. Unlike frequencies, means are used for scale-level variables.
For example, average salary or average test score provides insight into overall performance.
Example: Means by Group
Consider employee salary data:
| Department | Monthly_Salary |
|---|---|
| IT | 55000 |
| IT | 60000 |
| HR | 42000 |
| Sales | 50000 |
Calculating mean salary by department helps compare earning patterns.
MEANS TABLES=Monthly_Salary BY Department.
Understanding Crosstabs
Crosstabs (cross-tabulations) analyze relationships between two categorical variables.
They are widely used in surveys, market research, and social sciences.
Crosstabs answer questions such as:
- How does gender vary by department?
- How do responses differ by region?
Example: Crosstab Table
Imagine a dataset with Gender and Department:
| Department | Male | Female |
|---|---|---|
| IT | 3 | 1 |
| HR | 1 | 2 |
| Sales | 2 | 1 |
This table shows how gender distribution varies across departments.
CROSSTABS
/TABLES=Gender BY Department
/CELLS=COUNT ROW.
Interpreting the Results
Correct interpretation is essential:
- Frequencies show distribution
- Means show central tendency
- Crosstabs show relationships
These tools together provide a complete descriptive picture of data.
Quiz 1
Which analysis is best for categorical variables?
Frequencies.
Quiz 2
What does a mean represent?
The average value.
Quiz 3
Which analysis shows relationships between categories?
Crosstabs.
Quiz 4
Why are percentages useful in frequency tables?
They make comparisons easier.
Quiz 5
Which SPSS command produces cross-tabulations?
CROSSTABS.
Mini Practice
Create a dataset with:
- Gender
- Department
- Monthly_Salary
Perform:
- Frequencies for Gender
- Mean Salary by Department
- Crosstab between Gender and Department
Use Frequencies, Means, and Crosstabs from Analyze → Descriptive Statistics.
What’s Next
In the next lesson, you will learn how to create charts such as bar, pie, and histograms to visually represent statistical data.